Resumen de Proof as a means of discovery

Michael de Villiers

• This short note presents and discusses an interesting area partition result related to a parallelogram. It is, then, shown how proving the result, and understanding why the result is true based on the principle of conservation of the area of triangles with the same base and between the same parallel lines, leads to further generalizations to pentagons, hexagons, etc. The activity could be used in classroom at high school level, or in mathematics teacher education, preferably with dynamic geometry to illustrate the discovery function of proof.